Question: Solve for $x$ and $y$ using elimination. ${-x+5y = -5}$ ${x-6y = 4}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x+5y = -5}\thinspace$ to find $x$ ${-x + 5}{(1)}{= -5}$ $-x+5 = -5$ $-x+5{-5} = -5{-5}$ $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {x-6y = 4}\thinspace$ and get the same answer for $x$ : ${x - 6}{(1)}{= 4}$ ${x = 10}$